The current talk is concerned with the spectral theory, in particular, the principal eigenvalue theory, of nonlocal dispersal operators with time periodic dependence, and its applications. Nonlocal and random dispersal operators are widely used to model diffusion systems in applied sciences and share many properties. There are also some essential differences between nonlocal and random dispersal operators, for example, a random dispersal operator always has a principal eigenvalue, but a nonlocal dispersal operator may not have a principal eigenvalue. In this talk, I will present criteria for the existence of principal eigenvalues of nonlocal dispersal operators with time periodic dependence and consider the applications of the criteria to monostable equations with nonlocal dispersal.